Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics
Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics
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DOI：
10.1103/physrevb.99.235142
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发表时间：
2019-02
影响因子：
3.7
通讯作者：
Hongxia Hao;B. Rubenstein;Hao Shi
中科院分区：
文献类型：
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作者：
Hongxia Hao;B. Rubenstein;Hao Shi
在强关联多电子系统的研究中，Hubbard Kanamori（HK）模型已经成为过渡金属氧化物物理的原型之一。该模型是多带的性质，并包含洪德的耦合项，这对金属-绝缘体转变，高温超导性和其他物理性质有显着的影响。在下文中，我们提出了一个完整的理论框架，用于处理HK模型使用基态辅助场量子蒙特卡罗（AFQMC）方法和分析其性能的少带模型，其参数近似于观察到的那些在铼酸盐，铑酸盐，和其他材料展示洪德的物理。与以前的研究不同，约束路径和无相近似分别用于控制符号和相位问题，这使得高精度的HK模型的基态特性的参数范围内的实验兴趣的建模。我们表明，经过仔细考虑的Hubbard-Stratonovich变换和试用波函数，相对误差小于1%的能量可以常规实现中度到大的值的Hund的耦合常数。至关重要的是，我们的方法还准确地预测了磁有序和相变。提出的结果打开了大门，更多的预测模型的洪德的物理范围广泛的强相关材料使用AFQMC。
In the study of strongly-correlated, many-electron systems, the Hubbard Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model is multi-band in nature and contains Hund's coupling terms, which have pronounced effects on metal-insulator transitions, high-temperature superconductivity, and other physical properties. In the following, we present a complete theoretical framework for treating the HK model using the ground state Auxiliary Field Quantum Monte Carlo (AFQMC) method and analyze its performance on few-band models whose parameters approximate those observed in ruthenate, rhodates, and other materials exhibiting Hund's physics. Unlike previous studies, the constrained path and phaseless approximations are used to respectively control the sign and phase problems, which enables high accuracy modeling of the HK model's ground state properties within parameter regimes of experimental interest. We demonstrate that, after careful consideration of the Hubbard-Stratonovich transformations and trial wave functions employed, relative errors in the energy of less than 1% can routinely be achieved for moderate to large values of the Hund's coupling constant. Crucially, our methodology also accurately predicts magnetic ordering and phase transitions. The results presented open the door to more predictive modeling of Hund's physics within a wide range of strongly-correlated materials using AFQMC.